“ Logic does not allow you to say this”: is this assertion outdated?Does this proof resolve the Liar Paradox?Every sentence in propositional logic can be written in Conjunctive Normal FormInterpretation of relations in varying-domain models of F.O. modal logicNotion of truth in logicAccording to “Language, Proof, and Logic” $a=a$ is not a tautology. Why not?How can this contradiction be valid?Is a true contradiction possible in FOL?Semantics of Tautological EntailmentIs the Exclusive Disjunction really a Truth Function?Does it even make sense in logic to talk about interpretations that aren't true/false assignments?
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“ Logic does not allow you to say this”: is this assertion outdated?
Does this proof resolve the Liar Paradox?Every sentence in propositional logic can be written in Conjunctive Normal FormInterpretation of relations in varying-domain models of F.O. modal logicNotion of truth in logicAccording to “Language, Proof, and Logic” $a=a$ is not a tautology. Why not?How can this contradiction be valid?Is a true contradiction possible in FOL?Semantics of Tautological EntailmentIs the Exclusive Disjunction really a Truth Function?Does it even make sense in logic to talk about interpretations that aren't true/false assignments?
$begingroup$
I think one cannot say nowadays without further qualification " geometry does not allow you to say that the sum of a triangle's angles is less than 180 degrees".
The sentence concerning the sum of the angles of a triangle is false in euclidian geometry, but not in geometry in general.
Is the situation analogous in logic? Would it be outdated to say, to someone that contradicts himself/ herself : " Logic does not allow you to say this".
To continue the comparison, I think that euclidian geometry is the geometry that is the most comformable to our everyday experience of the physical world, the most "convenient" geometry for ordinary purposes, and in that sense, a sentence that does not agree with euclidian geometry can be said "false" ( where "false" means : not corresponding to the facts of the world such as we ordinarily experience it).
Can classical logic be considered as the remaining standard in the same sense?
logic nonclassical-logic
asked May 18 at 13:57
Eleonore Saint JamesEleonore Saint James
1,314118
$endgroup$
add a comment |
$begingroup$
I think one cannot say nowadays without further qualification " geometry does not allow you to say that the sum of a triangle's angles is less than 180 degrees".
The sentence concerning the sum of the angles of a triangle is false in euclidian geometry, but not in geometry in general.
Is the situation analogous in logic? Would it be outdated to say, to someone that contradicts himself/ herself : " Logic does not allow you to say this".
To continue the comparison, I think that euclidian geometry is the geometry that is the most comformable to our everyday experience of the physical world, the most "convenient" geometry for ordinary purposes, and in that sense, a sentence that does not agree with euclidian geometry can be said "false" ( where "false" means : not corresponding to the facts of the world such as we ordinarily experience it).
Can classical logic be considered as the remaining standard in the same sense?
logic nonclassical-logic
asked May 18 at 13:57
Eleonore Saint JamesEleonore Saint James
1,314118
$endgroup$
4
$begingroup$
Note that beyond Henning's great answer, in maths there is nothing you're not “allowed“ to say : you're allowed to say anything, some of it will be false, some of it will be true, some of it neither. If you say something unjustified, it will count as an assumption you're making (some of these assumptions can be contradictory, but you're still allowed to make them)
$endgroup$
– Max
May 18 at 15:13
4
$begingroup$
@Max: And, sometimes, people have made "obviously false" (or at least highly unconventional) assumptions and then gone on to develop entire new branches of mathematics from those assumptions. Non-Euclidean geometry is one example, but you also have the p-adic numbers, the complex numbers, and many other cases.
$endgroup$
– Kevin
May 18 at 18:48
add a comment |
$begingroup$
I think one cannot say nowadays without further qualification " geometry does not allow you to say that the sum of a triangle's angles is less than 180 degrees".
The sentence concerning the sum of the angles of a triangle is false in euclidian geometry, but not in geometry in general.
Is the situation analogous in logic? Would it be outdated to say, to someone that contradicts himself/ herself : " Logic does not allow you to say this".
To continue the comparison, I think that euclidian geometry is the geometry that is the most comformable to our everyday experience of the physical world, the most "convenient" geometry for ordinary purposes, and in that sense, a sentence that does not agree with euclidian geometry can be said "false" ( where "false" means : not corresponding to the facts of the world such as we ordinarily experience it).
Can classical logic be considered as the remaining standard in the same sense?
logic nonclassical-logic
asked May 18 at 13:57
Eleonore Saint JamesEleonore Saint James
1,314118
$endgroup$
I think one cannot say nowadays without further qualification " geometry does not allow you to say that the sum of a triangle's angles is less than 180 degrees".
The sentence concerning the sum of the angles of a triangle is false in euclidian geometry, but not in geometry in general.
Is the situation analogous in logic? Would it be outdated to say, to someone that contradicts himself/ herself : " Logic does not allow you to say this".
To continue the comparison, I think that euclidian geometry is the geometry that is the most comformable to our everyday experience of the physical world, the most "convenient" geometry for ordinary purposes, and in that sense, a sentence that does not agree with euclidian geometry can be said "false" ( where "false" means : not corresponding to the facts of the world such as we ordinarily experience it).
Can classical logic be considered as the remaining standard in the same sense?
logic nonclassical-logic
logic nonclassical-logic
asked May 18 at 13:57
Eleonore Saint JamesEleonore Saint James
1,314118
asked May 18 at 13:57
Eleonore Saint JamesEleonore Saint James
1,314118
edited May 18 at 14:07
Eleonore Saint James
asked May 18 at 13:57
Eleonore Saint JamesEleonore Saint James
1,314118
asked May 18 at 13:57
Eleonore Saint JamesEleonore Saint James
1,314118
asked May 18 at 13:57
Eleonore Saint JamesEleonore Saint James
1,314118
1,314118
4
$begingroup$
Note that beyond Henning's great answer, in maths there is nothing you're not “allowed“ to say : you're allowed to say anything, some of it will be false, some of it will be true, some of it neither. If you say something unjustified, it will count as an assumption you're making (some of these assumptions can be contradictory, but you're still allowed to make them)
$endgroup$
– Max
May 18 at 15:13
4
$begingroup$
@Max: And, sometimes, people have made "obviously false" (or at least highly unconventional) assumptions and then gone on to develop entire new branches of mathematics from those assumptions. Non-Euclidean geometry is one example, but you also have the p-adic numbers, the complex numbers, and many other cases.
$endgroup$
– Kevin
May 18 at 18:48
add a comment |
4
$begingroup$
Note that beyond Henning's great answer, in maths there is nothing you're not “allowed“ to say : you're allowed to say anything, some of it will be false, some of it will be true, some of it neither. If you say something unjustified, it will count as an assumption you're making (some of these assumptions can be contradictory, but you're still allowed to make them)
$endgroup$
– Max
May 18 at 15:13
4
$begingroup$
@Max: And, sometimes, people have made "obviously false" (or at least highly unconventional) assumptions and then gone on to develop entire new branches of mathematics from those assumptions. Non-Euclidean geometry is one example, but you also have the p-adic numbers, the complex numbers, and many other cases.
$endgroup$
– Kevin
May 18 at 18:48
4
4
$begingroup$
Note that beyond Henning's great answer, in maths there is nothing you're not “allowed“ to say : you're allowed to say anything, some of it will be false, some of it will be true, some of it neither. If you say something unjustified, it will count as an assumption you're making (some of these assumptions can be contradictory, but you're still allowed to make them)
$endgroup$
– Max
May 18 at 15:13
$begingroup$
Note that beyond Henning's great answer, in maths there is nothing you're not “allowed“ to say : you're allowed to say anything, some of it will be false, some of it will be true, some of it neither. If you say something unjustified, it will count as an assumption you're making (some of these assumptions can be contradictory, but you're still allowed to make them)
$endgroup$
– Max
May 18 at 15:13
4
4
$begingroup$
@Max: And, sometimes, people have made "obviously false" (or at least highly unconventional) assumptions and then gone on to develop entire new branches of mathematics from those assumptions. Non-Euclidean geometry is one example, but you also have the p-adic numbers, the complex numbers, and many other cases.
$endgroup$
– Kevin
May 18 at 18:48
$begingroup$
@Max: And, sometimes, people have made "obviously false" (or at least highly unconventional) assumptions and then gone on to develop entire new branches of mathematics from those assumptions. Non-Euclidean geometry is one example, but you also have the p-adic numbers, the complex numbers, and many other cases.
$endgroup$
– Kevin
May 18 at 18:48
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
I think the situation is fairly analogous between "logic" and "geometry", but your assumption about what the situation is for "geometry" is wrong.
It is entirely common and non-controversial that one can say "geometry" without any further qualification when one is implicitly speaking about Euclidean plane or solid geometry only. If one wants to speak about other geometries, it is generally expected to warn the reader/listener of this first.
This is not any deep claim about what really "is", simply a convenient convention about the use of language.
Similarly, when you say "logic" without further qualification, it will usually be assumed that you mean classical first-order logic or classical propositional logic (which is effectively a subsystem) -- or possibly the kind of usual quasi-formal mathematical reasoning that classical first-order logic aims to encode.
The fact that we know many other specialized kinds of logic has not displaced what the word usually refers to.
answered May 18 at 14:08
Henning MakholmHenning Makholm
247k17318563
$endgroup$
$begingroup$
Fantastic answer. Couldn't have said it better myself.
$endgroup$
– Don Thousand
May 18 at 14:32
add a comment |
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1 Answer
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1 Answer
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$begingroup$
I think the situation is fairly analogous between "logic" and "geometry", but your assumption about what the situation is for "geometry" is wrong.
It is entirely common and non-controversial that one can say "geometry" without any further qualification when one is implicitly speaking about Euclidean plane or solid geometry only. If one wants to speak about other geometries, it is generally expected to warn the reader/listener of this first.
This is not any deep claim about what really "is", simply a convenient convention about the use of language.
Similarly, when you say "logic" without further qualification, it will usually be assumed that you mean classical first-order logic or classical propositional logic (which is effectively a subsystem) -- or possibly the kind of usual quasi-formal mathematical reasoning that classical first-order logic aims to encode.
The fact that we know many other specialized kinds of logic has not displaced what the word usually refers to.
answered May 18 at 14:08
Henning MakholmHenning Makholm
247k17318563
$endgroup$
$begingroup$
Fantastic answer. Couldn't have said it better myself.
$endgroup$
– Don Thousand
May 18 at 14:32
add a comment |
$begingroup$
I think the situation is fairly analogous between "logic" and "geometry", but your assumption about what the situation is for "geometry" is wrong.
It is entirely common and non-controversial that one can say "geometry" without any further qualification when one is implicitly speaking about Euclidean plane or solid geometry only. If one wants to speak about other geometries, it is generally expected to warn the reader/listener of this first.
This is not any deep claim about what really "is", simply a convenient convention about the use of language.
Similarly, when you say "logic" without further qualification, it will usually be assumed that you mean classical first-order logic or classical propositional logic (which is effectively a subsystem) -- or possibly the kind of usual quasi-formal mathematical reasoning that classical first-order logic aims to encode.
The fact that we know many other specialized kinds of logic has not displaced what the word usually refers to.
answered May 18 at 14:08
Henning MakholmHenning Makholm
247k17318563
$endgroup$
$begingroup$
Fantastic answer. Couldn't have said it better myself.
$endgroup$
– Don Thousand
May 18 at 14:32
add a comment |
$begingroup$
I think the situation is fairly analogous between "logic" and "geometry", but your assumption about what the situation is for "geometry" is wrong.
It is entirely common and non-controversial that one can say "geometry" without any further qualification when one is implicitly speaking about Euclidean plane or solid geometry only. If one wants to speak about other geometries, it is generally expected to warn the reader/listener of this first.
This is not any deep claim about what really "is", simply a convenient convention about the use of language.
Similarly, when you say "logic" without further qualification, it will usually be assumed that you mean classical first-order logic or classical propositional logic (which is effectively a subsystem) -- or possibly the kind of usual quasi-formal mathematical reasoning that classical first-order logic aims to encode.
The fact that we know many other specialized kinds of logic has not displaced what the word usually refers to.
answered May 18 at 14:08
Henning MakholmHenning Makholm
247k17318563
$endgroup$
I think the situation is fairly analogous between "logic" and "geometry", but your assumption about what the situation is for "geometry" is wrong.
It is entirely common and non-controversial that one can say "geometry" without any further qualification when one is implicitly speaking about Euclidean plane or solid geometry only. If one wants to speak about other geometries, it is generally expected to warn the reader/listener of this first.
This is not any deep claim about what really "is", simply a convenient convention about the use of language.
Similarly, when you say "logic" without further qualification, it will usually be assumed that you mean classical first-order logic or classical propositional logic (which is effectively a subsystem) -- or possibly the kind of usual quasi-formal mathematical reasoning that classical first-order logic aims to encode.
The fact that we know many other specialized kinds of logic has not displaced what the word usually refers to.
answered May 18 at 14:08
Henning MakholmHenning Makholm
247k17318563
edited May 18 at 14:45
answered May 18 at 14:08
Henning MakholmHenning Makholm
247k17318563
answered May 18 at 14:08
Henning MakholmHenning Makholm
247k17318563
answered May 18 at 14:08
Henning MakholmHenning Makholm
247k17318563
247k17318563
$begingroup$
Fantastic answer. Couldn't have said it better myself.
$endgroup$
– Don Thousand
May 18 at 14:32
add a comment |
$begingroup$
Fantastic answer. Couldn't have said it better myself.
$endgroup$
– Don Thousand
May 18 at 14:32
$begingroup$
Fantastic answer. Couldn't have said it better myself.
$endgroup$
– Don Thousand
May 18 at 14:32
$begingroup$
Fantastic answer. Couldn't have said it better myself.
$endgroup$
– Don Thousand
May 18 at 14:32
add a comment |
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$begingroup$
Note that beyond Henning's great answer, in maths there is nothing you're not “allowed“ to say : you're allowed to say anything, some of it will be false, some of it will be true, some of it neither. If you say something unjustified, it will count as an assumption you're making (some of these assumptions can be contradictory, but you're still allowed to make them)
$endgroup$
– Max
May 18 at 15:13
4
$begingroup$
@Max: And, sometimes, people have made "obviously false" (or at least highly unconventional) assumptions and then gone on to develop entire new branches of mathematics from those assumptions. Non-Euclidean geometry is one example, but you also have the p-adic numbers, the complex numbers, and many other cases.
$endgroup$
– Kevin
May 18 at 18:48